1. What is Double-Precision Floating Point?

Double-precision floating-point is a computer number format that occupies 64 bits in computer memory. It represents a wide range of values by using a sign bit, exponent, and fraction (mantissa).

2. How Does the Conversion Work?

The conversion uses the IEEE 754 standard formula:

Where:

• \( s \) — Sign bit (0 for positive, 1 for negative)
• \( e \) — 11-bit exponent (biased by 1023)
• \( f \) — 52-bit fraction (mantissa)

Explanation: The formula breaks down the 64-bit representation into its components and reconstructs the original value.

3. Importance of Floating Point Representation

Details: Understanding floating-point representation is crucial for numerical computing, financial calculations, and scientific applications where precision matters.

4. Using the Calculator

Tips: Enter any decimal number to see its 64-bit double-precision floating-point representation, including sign, exponent, and fraction components.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of double-precision floats?
A: Approximately ±2.23×10^-308 to ±1.80×10^308 with 15-17 significant digits.

Q2: Why does 0.1 + 0.2 not equal 0.3 exactly?
A: Because many decimal fractions can't be represented exactly in binary floating-point.

Q3: What are special values in floating-point?
A: ±0, ±infinity, and NaN (Not a Number) are special representations.

Q4: What's the difference between single and double precision?
A: Single uses 32 bits (7-8 significant digits), double uses 64 bits (15-17 digits).

Q5: How are very small numbers represented?
A: Through denormal numbers when the exponent is 0 (allowing gradual underflow).